Bank of England governor Sir Mervyn King is likely to signal on Wednesday that he stands ready to unleash a fresh round of quantitative easing if the economy fails to bounce back, after news that inflation dropped sharply last month, to 3.6%.

The office for national statistics said the consumer price index had declined from 4.2% in December, to 3.6%, its lowest level since November 2010, as the impact of the coalition's VAT rise dropped out of the annual comparison.

"The confirmation that inflation is falling is likely to encourage the MPC to continue to gradually expand QE in order to give more support to the economy," said Michael Saunders, UK economist at Citi.

King has long predicted that inflation would start to fall back towards the Bank's 2% target once one-off effects such as the VAT rise and last year's spike in oil prices started to ease.

But when he sets out his latest assessment of the prospects for the economy at quarterly inflation report briefing on Wednesday, the governor is likely to repeat the sobering message, spelled out in an open letter to the chancellor, that, "although inflation is now falling broadly as expected, the process of rebalancing still has a long way to go. Growth remains weak and unemployment is high."

Under the terms of the Bank's independence, laid down by Gordon Brown in 1997, the governor must write to the chancellor each time inflation remains more than 1 percentage point above or below the government's 2% target for more than three months.

The missive was the eighth time King has written to Osborne since the coalition took power.

"The unwelcome contribution of sluggish growth and high inflation over the past two years is a reflection of the need for the economy to rebalance following the financial crisis and associated deep recession, together with rises in the costs of energy and imports," King wrote.

The Bank's monetary policy committee expects inflation to fall rapidly throughout 2012. At its February policy meeting, it announced a £50bn increase in its asset purchase programme, taking the total of electronic money it has spent on trying to boost the economy to £325bn.

Howard Archer, of the consultancy IHS Global Insight, said there should be a fresh decline in February, because many shops delayed passing on last year's VAT increase until the end of the January sales. "Consumer price inflation should fall appreciably further," he added. VAT was increased from 17.5% to 20% last year as part of George Osborne's deficit-reduction plan.

However, Brendan Barber, general secretary of the TUC, stressed that despite the decline in inflation, living standards are still falling for many in Britain. "With prices still increasing twice as fast as wages, workers are still getting poorer month-by-month while high unemployment and wage stagnation persists," he said.

But King also used his letter to warn the chancellor that "there is a limit to what monetary policy can achieve."

Osborne replied that monetary policy is "the first line of defence in the face of economic shocks", and insisted that the government's deficit reduction strategy had created the room for the Bank to act.

Retailers have been forced into discounting amid tough trading conditions on the high street. Over the past two months, inflation has fallen by 1.2 percentage points. The ONS said that was a larger decline over two months than at any time since 2008, when Alistair Darling cut VAT as part of his emergency rescue package.

On the wider retail price index measure, which includes housing costs, inflation fell to 3.9%, from 4.8% in December, the ONS said.

Official UK unemployment stands at 2.67 million – but depending what you count, could be as low as 1.6 million or more than 11 million. James Ball, with your help, digs into the figures. Get in touch below the line, email your views to james.ball@guardian.co.uk or tweet @jamesrbuk